API

neural_schrodinger.bin_to_float(binary)

Converts a binary number encoded with fixed point format. Here the first digit is reserved for sign and the rest are binary places starting with 2^1 and decreasing. Here we use ten bits to encode a number.

Parameters:

binary : string

A string of ten digits representing the number in binary fixed point format.

Returns:

number : float

A float that corresponds to the fixed point binary format.

neural_schrodinger.breed_genes(gene1, gene2)

Mates two genes using the uniform crossover algorithm.

Parameters:

gene1 : string

The string representing the first gene to mate

gene2 : string

The string representing the second gene to mate.

Returns:

newgene : string

The child of the two mated strings

neural_schrodinger.eigenfunction(net, x)

Converts the two outputs of the neural network to the value of the wavefunction at x.

Parameters:

net : PyBrain FeedForwardNetwork

The neural network that represents the wavefunction.

x : float

The location at which one wants to evaluate the wavefunction.

Returns:

wavefunction : float

The value of the wavefunction at x

neural_schrodinger.eigenfunction_second_deriv(net, x)

Calculates the second derivative of the wavefunction represented by net.

Parameters:

net : PyBrain FeedForwardNetwork

The neural network representing the wavefunction.

x : float

The location at which one wishes to evaluate the wavefunction.

neural_schrodinger.float_to_bin(number)

Converts a floating point number to a ten bit fixed point format as specified in bin_to_float.

Parameters:

number : float

The floating point number to convert.

Returns:

binary : string

A string representing the binary encoding of the floating point number in ten bit fixed point format.

neural_schrodinger.gene_fitness(gene, net, points, mass)

Calculates the fitness of the gene based on the difference between the energy and the hamiltonian applied to the wavefunction squared evaluated at the points specified by points.

Parameters:

gene : string

The gene with which one wishes to get the fitness of.

net : PyBrain FeedForwardNetwork

The neural network used to represent the wavefunction.

points : array of floats

An array of random points with which one wishes to evaluate the hamiltonian.

mass : float

The reduced mass of the harmonic oscillator system.

Returns:

float

The fitness of the gene.

neural_schrodinger.gene_to_system(gene)

Converts a gene to a system which corresponds to a set of neural network weights and an energy.

Parameters:

gene : string

A string representing the binary encoding of the system

Returns:

weights,energy : (float list,float)

A tuple containing the weights and energy of the system.

neural_schrodinger.get_random_gene(gene_length)

Returns a random gene which corresponds to a random binary sequence of length specified by gene_length.

Parameters:

gene_length : int

Length og the random gene to generate

Returns:

gene : string

A string representing a random gene of length gene_length

neural_schrodinger.get_random_points(xmin, xmax, M)

Gets n random points between xmin and xmax used for the random point evaluation method.

Parameters:

xmin : float

Minimum value that the points can take.

xmax : float

Maximum value that the points can take.

M : int

The number of points to generate.

Returns:

array of floats

An array of M random points.

neural_schrodinger.get_weights_by_layer(net, layername)

Get the weights of the layer specified by layername of a PyBrain neural network net.

Parameters:

net : PyBrain FeedForwardNetwork

A feed forward neural network created using PyBrain

layername : string

A string specifying the name of the layer that one wishes to get the weights of.

Returns:

weights : numpy array of floats

A Numpy array of floats containing the weights of the specified layer.

neural_schrodinger.hamiltonian(net, x, mass)

Calculates the hamiltonian of a harmonic oscillator of reduced mass “mass” applied to the wavefunction represented by net.

Parameters:

net : PyBrain FeedForwardNetwork

The neural network that represents the wavefunction one wishes to apply the hamiltonian to.

x : float

The location at which one wishes to get the value of the hamiltonian

mass : float

The reduced mass of the harmonic oscillator

Returns:

float

The value of the hamiltonian applied to the wavefunction

neural_schrodinger.initialize_nn()

Initializes a neural network using PyBrain with 6 hidden layers, 1 input layerm and 2 output layers.

neural_schrodinger.natural_selection(genes, net, num_survivors, points, mass)

Applies “natural selection” to a list of genes using the tournament methodology. In this methodology genes are pitted against each other in pairs and the gene with the greatest fitness wins. This continues until the specified amount of genes are obtained.

Parameters:

genes : list of strings

A list of strings each of which corresponds to a gene.

net : PyBrain FeedForwardNetwork

The neural network used to approximate the wavefunction

num_survivors : int

The number of survivors that are desired to be left.

points : array of floats

A set of points one wishes to evaluate the genes fitness on.

mass : float

The reduced mass used in the Schrodinger equation to evaluate fitness.

Returns:

survivors, survivor_fitnesses : (list of strings, list of floats)

A list of survivor genes and their associated fitnesses.

neural_schrodinger.nn_array(net, array)

Apply the neural network over an array.

Parameters:

net : PyBrain FeedForwardNetwork

Neural network to apply over an array.

array : array of floats

Array of floats to activate the neural network over

Returns:

array of floats

The output of the neural network for each element of the array

neural_schrodinger.nn_first_derivative(net, x)

The first derivative of a feedforward neural network with one hidden sigmoid layer.

Parameters:

net : PyBrain FeedForwardNetwork

The neural network one wishes to get the first derivative of.

x : float

The location x where one wants the derivative

Returns:

output1_derivative, output2_derivative : (float,float)

The first derivative of the first and second output of the neural network.

neural_schrodinger.nn_second_derivative(net, x)

The second derivative of a feedforward neural network with one hidden sigmoid layer.

Parameters:

net : PyBrain FeedForwardNetwork

The neural network one wishes to get the first derivative of.

x : float

The location x where one wants the derivative

Returns:

output1_derivative, output2_derivative : (float,float)

The second derivative of the first and second output of the neural network.

neural_schrodinger.system_to_gene(net, energy)

Converts a system specified by the given PyBrain neural network and energy to a binary encoding specified by float_to_bin.

Parameters:

net : PyBrain FeedForwardNetwork

A PyBrain neural network that corresponds to the wavefunction guess

energy : float

The guessed energy that corresponds to the given neural network

Returns:

string

A string which specifies the binary encoding of the given system.

neural_schrodinger.weights_to_binary(net)

Converts the weights of a PyBrain neural network to the binary encoding specified by float_to_bin.

Parameters:

net : PyBrain FeedForwardNetwork

Returns:

gene : string

A string that corresponds to the binary encoding of the neural network which corresponds to the binary encoding of the neural network weights.